As an important follow-up report on the latest study of the first author (H.S.) on an off-shell quantum field causing a dressed photon and dark energy, we further discuss a couple of intriguing subjects based on our new theory. One is the dressed photon constant. If we use it, in addition to h¯ and c, as the third component of natural units, then it is defined as the geometric mean of the smallest and the largest lengths: Planck length and that relating to the cosmological constant. Interestingly, this length (≈ 50 nanometers) seems to give a rough measure of the Heisenberg cut for electromagnetic phenomena. The other is a new perspective on cosmology that combines two original notions, i.e., twin universes and conformal cyclic cosmology, proposed respectively by Petit and Penrose, into one novel picture where universes expand self-similarly. We show the possibility that twin universes having a dual structure of [matter with (dark energy & matter)] vs. corresponding anti-entities, separated by an event horizon embedded in the geometric structure of de Sitter space, undergo endless cyclic processes of birth and death, as in the case of the pair creation and annihilation of elementary particles through the intervention of a conformal light field.

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two variable models, where, , is Newton’s constant, and, , increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/ zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.